# calculus

Use the demand function
X=325(1-(6p/7p+4)) to find the rate of change in the demand x for the given price p=\$5.00. Round your answer to two decimal places.

A. 5.13 UNITS PER DOLLAR
B. -0.85 UNITS PER DOLLAR
C. 0.85 UNITS PER DOLLAR
D. 1.35 UNITS PER DOLLAR
E. -5.13 UNITS PER DOLLAR

1. 👍
2. 👎
3. 👁
1. Setting u(p) = 6p and v(p)=7p+4, we have x=325(1-u/v). So,

dx/dp = -325 (uv'-u'v)/v^2
= -325(6p(7)-6(7p+4)/(7p+4)^2
= -325(42p-42p-24)/(7p+4)^2
= 325*24/(7p+4)^2

x'(5) = 32*24/39^2 = 5.13

1. 👍
2. 👎

## Similar Questions

1. ### Economic

Suppose that labor is the only input used by a perfectly competitive firm that can hire workers for \$50 per day. The firm’s production function is as follows: Days of Labor/Units of Output: 0/0, 1/7, 2/13, 3/19, 4/25, 5/28,

2. ### math help

Universal instruments found that the monthly demand for its new line of Galaxy Home Computers t months after placing the line on the market was given by D(t) = 2900 − 2300e−0.08t (t > 0) Graph this function and answer the

3.) The demand equation for a certain product is q=500-40p+p^2 where p is the price per unit (in dollars) and q is the quantity of units demanded (in thousands). Find the point elasticity of demand when p = 15. If this price of 15

4. ### Math

Could someone work this question out so I understand it. Thanks The marginal price dp/dx at x units of demand per week is proportional to the price p. There is no weekly demand at a price of \$100 per unit [p(0)=100], and there is

1. ### Economics

Read the statement. Economists note that personal income rose by 5 percent last year. What impact will the change in personal income have on-demand? A. It will cause the demand curve to shift down. B. It will cause the demand

2. ### Calc

Find the elasticity of demand​ (E) for the given demand function at the indicated values of p. Is the demand​ elastic, inelastic, or neither at the indicated​ values? q=410 - 0.2 p^2 a.​\$21 b.\$39

3. ### Math - Limits/Derivatives

The demand x is the number of items that can be sold at a price of \$p. For x = p^3 - 4p + 400, find the rate of change of p with respect to x by differentiating implicitly.

4. ### Math

The demand equation for a product is: q=60/p + ln(65-p^3) A) Determine the point of elasticity of demand when p=4, and classify the demand as elastic, inelastic, or of unit elasticity at this price level. B) If the price is

1. ### Further calculus

1) A price p (in dollars) and demand x for a product are related by 2x^2+6xp+50p^2=10600. If the price is increasing at a rate of 4 dollars per month when the price is 30 dollars, find the rate of change of the demand. 2) a) The

2. ### Math - Limits/Derivatives

If a price-demand equation is solved for p, then price is expressed as p = g(x) and x becomes the independent variable. In this case, it can be shown that the elasticity of demand is given by E(x) = - [g(x) / xg'(x)]. Use the

3. ### Calculus

Given the demand function q=173-5p, determine the price where demand has unit elasticity.

4. ### Economics

Help me with this, please. Read the statement. Economists note that personal income rose by 5 percent last year. What impact will the change in personal income have on-demand? It will cause the demand curve to shift down. It will